Question

# In the case of electrons and photons having the same wavelength, what is the same for them? A. EnergyB. VelocityC. Momentum D. Angular momentum

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Hint: Equate the de Broglie wavelength of both electrons and protons and solve the question.

Complete step by step solution:
Given, the wavelength of electrons and photons are the same.
Now, the wavelength of electrons are given by ${\lambda _e}$ and the wavelength of protons are given by ${\lambda _p}$.
Thus , the wavelength of electrons = the wavelength of protons
${\lambda _e} = {\lambda _p}$
From de Broglie wavelength, we know that $\lambda = \dfrac{h}{p}$
Therefore,
$\dfrac{h}{{{p_e}}} = \dfrac{h}{{{p_p}}} \\ \Rightarrow \dfrac{1}{{{p_e}}} = \dfrac{1}{{{p_p}}} \\ \Rightarrow {p_e} = {p_p} \\$

Thus , the velocity of electrons and protons will be the same .

Hence, the required option is C - momentum.

Note: From de Broglie wavelength , we know that the wavelength of a microscopic particle can be given by $\lambda = \dfrac{h}{p}$ where $\lambda$ is the wavelength of given particle, h is Planck’s constant which is equal to $6.626 \times {10^{ - 34}}{m^2}kg/s$ and p is momentum of the given particle. Before solving the question, it needs to be understood conceptually.